Hyperbolic curve plotting apparatus



Oct.'2, 1945. E. McKABA I 2,385,827

I HYPERBOLIC CURVE PLOTTING APPARATUS Filed Nov. 27, 1943 F1s-l Patented Oct. 2, 1945 HYPERBOLIC CURVE PLOTTIN G APPARATUS Edward McKaba, Brooklyn, N. Y.

Application November 27, 1943, Serial No. 511,929

(Granted under the act of March 3, 1883, as amended April 30, 1928; 370 O. G. 757) 6 Claims.

Theinvention described herein may be manufactured and used by or for the Government for governmental purposes, without the payment to me of any royalty thereon.

This invention relates to apparatus for drawing geometrical curves, and more particularly to a device for plotting hyperbolas, a curve in which the difference in distance from any point on the curve to two fixed fool is always constant, and has for an object the provision of scale means together with two associated foci points and an associated curve plotting means whereby the constant difference between the foci and curve may be selected on the scale and movement of the curve plotting means will describe a hyperbolic curve.

A principal purpose of this invention is the provision of an apparatus for graphically recording the location of an impact or explosion from a previously obtained sound-ranging record. In this application the time of the arrival of the impact or explosive sound at two or more spaced sound detectors is recorded, and by multiplying the time-difierence of the reception of the sound by the velocity of the sound wave, a distancedifierence figure is obtained. This distance-difference between the impact and the detectors is set off relative to the scale between two foci points on a plotting surface as the constant of the hyperbolic curve to be drawn. The hyperbola is plotted on the surface by my improved curve describing device, and the relative point of the impact or explosion will be graphically plotted to lie somewhere along this line or curve.

By utilizing a third detector station and plotting a second curve on the plotting surface with tion and one of the other stations as the second pair of foci points on the plotting surface, another line or curve may be drawn, intersecting the first line. The intersection of the two lines, or curves, will graphically indicate on the plotting board the exact impact or explosion point on the plotting surface with relation to the foci points.

A further object is the provision of a simple, inexpensive curve plotting apparatus, including a tim'e-difierence'reference scale, a singleflexible control member associated with said scale at opposite ends thereof, including means for simultaneously and uniformly allowing equal movements only of the control member with respect to the opposite ends of the scale, and scribing means adjustably secured to the flexible control member for adjustment thereonrelative to the reference scale.

Figure 1 is a fragmentary plan view, illustrating a portion of a plotting board having my improved curve plottin device applied thereto, the curve plotting device being shown in full lines at the start of a hyperbola plotting operation, and in dotted line at the termination of the said plotting operation.

Fi ure 2 is a fragmentary rear view of the plotting board, disclosing more particularly the flexible curve plotting means and tensioning means therefor, for causing equal uniform movement of the curve plotting means at the focal points of the hyperbola to be plotted, located at the opposite ends of the scale. I Figure 3 is an edge View of a portion'of the plotting board showing the cable and winding drum arrangement, parts being broken away and shown in section; and

Figure 4 is a fragmentary detail view of the stylus member.

Referring to the drawing, l indicates a curve plotting surface or table having a distance-dif ference scale delineated thereon, indicated at 2, and relatively representing the distance between two sound detectors located at predetermined spaced points on a bombing field between which points a bomb or explosion is to be recorded. The scale is divided uniformly from a central zero point 3 in opposite directions, representing the point between the two sound detectors on the A third sound detector is also preferably placed on the'field and spaced from the other detectors at a distance equal to the distance between the first two detectors forming an equilateral triangle between the three detectors, with the point of impact or explosion to be recorded located within the triangle. Fourvdetectors may also be used, if

I desired, at the four corners of an equal-sided rectangular outline or target area, each side of the rectangle being represented on the plotting board as the distance between the ends of the scale 2.

Located at the opposite ends of the scale, and representing the distance between any two adjacent sound or impact detectors on one side of the triangular or rectangular bombing field and the foci of a hyperbola on the plotting board, are two small apertures or passages 4 and 5 for receiving the elongated flexible plotting member or cord 6. This cord is preferably of a fine non-stretching material, initially drawn taut across the plotting assess The cord'6passes through the openings 4 and 5, as best seen in Figures 2 and 3, and the opposite end portions of the cord are wound on two cable drums, or disks 1 and 1a, with the ends of the cords secured to the periphery of thedru nis,

The drums are secured together to move as a unit and have their peripheries grooved to receive the plotting cord, the end portion of one cord'being wound clockwise on one drum'whilethe end portion of the other cord is wound clockwise on the other drum.

' Tension means is provided 'forrotatablyftene sioning the drums I and la, providing asubstantially uniform and equal tension -on.both end portions of the cord B extending through the openings 4 and 5 and across the front ofthe plotting board. This tension means comprises a lever 8, having a cam shaped edge 9, preferably grooved to receive a spring loaded-tension cable l0,'which is attached. at one end to thefree end of the lever B, and .at its other end-to a'tension coil springv H, secured to a bracket member l2, fastened, to the rear of the plotting board 1 in any suitable manner; 1 Y r The lever B is fixed to the two disks ll and 1a, to rotate therewith as the cord B-is withdrawn from the drumsand as thetension is increased, dueto the expansion of the coil spring H, when the'cord 6 at the front-ofthe-plotting-=board'is moved laterally across the plotting surface, the contour of the cam portion 9,-receiving the tension cable Hi, gradually approached the-center of rotation of the arm 8, reducing-theleverage effect of the tensioning cable 10 with respect to the center of the disks I and Iain substantially direct ratio to the increase in tension inthe spring H due to its elongation;thus maintaining the tension on the curve plotting cord "6' substantially constant, so that the forcerequired to pull the -p1otting--cord"6 is not increased as the point selected for plotting is moved farther from the straight line between'the' apertures li'andli. Y The cable control unit; consisting of thetwin disks |-la and the lever 8, is preferablyrotatably journalled on a fixed pivot'bearing' or'standard l3, which rotatably supports the unit in spaced relation to the back of the plotting board. [The end portions of the cable are brought through the plotting board apertures 4 and 5, into the planes of the cable grooves in the respective disks on which the able is wou d, through tubular conduit members M, in register with the openings 4 and 5, each conduit member having a pulley l5 journalled in a notch formed in thewall thereof over whichthe cable 6 is trained.

To plot a 'hyperbola, the plotting cord '8 is clamped or grasped at any point in its length between the openings 4 and 5, opposite to a desired distance-difference setting selected on the scale 2, and this point on the cable is then drawn across the plotting board I with the por tions of the cordbetween the point selected on the cable and therespective cable drums maintained taut as the cable is withdrawn irom the drums, The line traverseid by the point across and 5.

the plotting board describes a hyperbola for the distance-difference selected on the scale.

To aid in making a graphic recording of this curve on a sheet placed on the plotting board, a stylus member i5 is preferably used, which may be clamped, or otherwise adjustably secured to the plotting cable 6 at any desired distance-difference point, as selected on the fixed scale 2. The stylus member comprises a body having a pointed end 11 carrying a marking element such as a pen 7 or pencil i3 for drawing the curve on the plotting board when the stylus is displaced downwardly across the board. The stylus body is somewhat elongated, terminating in a handle portion I9, adaptedto be grasped between the thumb and forefinger of the hand of the operator, while the cable clamping means for adjustably securing the stylus member to the plotting cable at any desired point,-may be any type of clamping means such as that disclosed in the drawing and comprising a pin member zit-projecting from-the front face of thestylus body andganassociated inclined or cammin'g'sur'face 2| so arranged that the cable may be wedged-in between the pin 29 and the inclined surface 24.

- In the operation of: the'device, a sheet oi' paper is placed under the scale 2,.preferably of a-relative size and shape representing the edges of the field between the sound detectors from which the distance-difference figure is obtained.- -When three sound detectors are used,'-disposedo'n two sides of a rectangular field, equidistant from a third intermediate sound detector-in the corner of the field, a sheet representing the field is-first placed on the plotting board or surface with-two of its corners coinciding with the openings 4 Assuming that the relative distancedifference of the impact-or eXp'losion'o'f-a bomb or shell was at Son the scale 2 as recorded-by the sound detectors on one side-of the bombing held and closer to the sound recording-device represented by the opening 4 at the end of the sea-lei,

' the stylus member wou1d*be"s'ecured=toth plbt;

ting cord 6, asshown in full lines in Figure l; opposite 3 and nearer to the opening I, and'then drawn downwardly to the dotted line position "in that figure while keeping "the "longitudinal-axis of the stylus "member'in substantially-constant bisecting relation with respect to the angle formed by the portions of the cable that each sideof the stylus. The line scribed by the marking member [8 in the end of the stylus member, on the-sheet placed on the plotting board is a hyperbola,repi'esenting a curved line onthe'actual bombing field; and the impact point" where thebomb or shell landed will be somewhere on this hyperbola, as plotted on the board. o F

The plotting sheet on-the plotting board is now turned to dispose the relative location'of the sound detectors represented thereon, for the second pair of detectors, coincident with the open-i ings 4 and 5 in the plotting board and the stylus is now adjusted and secured to the 'cordlijto accord with the'distance-dirference of'the sound or impact as recorded .bythe second set of sound detectors, as indicated on the'sc'alel, 'The stylus is now drawn downwardlyas before, describing a second hyperbola which will intersect the first drawn hyperbola atsome point, and'the'intersection of the two hyperbolas willrecord on the plotting sheet on the board the exact relative location of the-impact or -explosion with-reference to the relative location of the sound recording, devices as indicated by the openings 4- 501; the

selected on the scale);

WhatI'claimis:

' L M 1. In a hyperbola plotting devic'e; a plotting board having Spaced plottin gcord; receiving guide openings formed thereinplocated 'at the foci of thehyperbola to be plotted; a'hyperbola plotting cord extendingbetween the guide-openings with its end portions" extending through and beyond the openings, rotary cord movement controlling meansmountedon the" plotting board comprising accord wind-ingdrum having both end portions of the co rd wound around the drum in the same peripheral direction with the ends secured to the drum, resilient means between the drum and said board for rotating the drum to maintain uniform tension on the cord plotting board and the-distance differen-ce figures between the guide openings, a distance-diiference reference scale between said guide openings, and a marking stylus having means for adjustably securing the stylus to the cord at any point between the cord receiving guide openings opposite a selected distance-difference reference point on the scale, for scribing a hyperbola on the plotting board with the point selected on the scale as the starting point of the hyperbola and the relatively different distances between the said point and the guide openings for the plotting cord constituting the distance between the foci and the hyperbola.

2. Ina hyperbola plotting apparatus, a support having a plotting board formed ,with spaced openings extending through the surface of the board to the rear thereof, located at the foci of the hyperbolas to be plotted, a distance-difference scale between the foci points having indicia thereon divided equally from a central point between the foci toward each of the foci, cable winding drum means rotatably mounted on the rear of the board between the guide openings, spring means for rotating said drum means in one direction, plotting cable means extending across the front of the board along said scale with the end portions of the cable slidably disposed through said guide openings and wound around the winding drum means in the same direction and secured to the drum to oppose rotation of the drum means by said spring means, and a stylus member adjustably secured to the cable by .the 'plotting cable and spring tension means between said tension cable and the support for tensioning the tension cable.

means intermediate thelspaced cable openings having a stylus point disposed adjacent the cable engaging portion of the stylus member for positioning the stylus on the cable with reference to a selected distance-difference point on the scale.

3. In a hyperbola plotting apparatus, a support having a plotting surface formed with two spaced openings therein and located at the foci points of a series of hyperbolas tobe described on the plotting surface, a plotting cord tensioned between the two openings with its end portions extending through the openings to the rear of the plotting surface, an adjustable stylus member adapted to be secured to the cord between the openings, a pair of cable drums rotatably mounted together as a unit on the support in the rear of the plotting surface with the end portions of the plotting cord wound around the drums in the same annular direction and their ends secured to the drums, a lever fixed to the drums for rotation therewith having a cam shaped tension cable receiving edge, a tension cable secured to the outer end of the lever, adapted to traverse the cam shaped tension cable receiving edge when the drums are rotated ,54. In a hyperbola curve plotting a'pparatus, a support having a curve plotting surface formed with spaced cable guide openings extending through the plotting surface, located at the focal points of any hyperbola to be plotted 'on the plot.- ting surface, a plotting cabletensioned between the; openings with its. end portions :extending through said openingsto'the rear of said plotting surface, a reference scale, disposed on the plotting surface between the two openings', .said scale having indicia indicating different focal distances between the two guide openings and hyperbolar curves to be drawn, a cable controlling unit at the rear of said plotting surface comprising a supporting standard, carrying twin cable winding and tensioning disks and an actuating lever for the disks, tension means for rotating said cable controlling unit in one direction comprising spring means secured to the support at one end, and to the disk actuating lever at its other end,

said plotting cable having each end portion wound around one of said disks in opposing relation to direction of movement of the disks caused by said tensioning means, whereby the tension means and cable controlling unit maintain the cable means in uniformly taut condition between openings in the plotting surface and cause equal movements of the cable through said opening when a point on the cable between said openings is moved across the plotting surface from any selected point on the scale, and a marking stylus 'adjustably disposed on plotting cable between said openings, said stylus including a pointer end for registration with the reference scale, and means for securing the stylus to the cable opposite any point on the reference scale, the distances between the point at which the stylus is secured on the plotting cable and the cable receiving openings constituting the location of the foci of the hyperbola to be drawn.

5. In a hyperbola curve plotting apparatus, a support having a curve plotting surface formed with spaced cable guide openings extending through the plotting surface located at the focal points of any hyperbola to be plotted on the plotting surface, a plotting cable tensioned between the openings with its end portions extending through said openings to the rear of said plotting surface, a plotting cable tensioning and controlling unit secured to the rear of said plotting surface comprising a supporting standard fixed to the rear of said plotting surface, concentric twin cable winding and tensioning discs rotatably mounted as a unit on said supporting standard, an actuating lever fixed at one end to the discs, tension means for rotating said plotting cable tensioning discs in one direction comprising extensible elongated spring means secured to the support at one end in spaced relation to the supporting standard, and to the twin cable winding and tension disc-actuating lever at the other end, said plotting cable having each end portion Wound around one of said discs and secured thereto in opposite relation to the direction of rotative movement of the twin discs by said tensioning means to maintain the cable taut between the openings in the plotted surface and permit only equal movements of the cable through said openings when any selected point on the cable between said openings at unequal distances from said cable guide openings is moved laterally across said plotting surface tocause said point to describe a hyperbola curve on said plotting surface. n V Y.

6. In a hyperbola; plotting device,la plotting boardhavingspace'd plotting cord receivingguide means thereon located at the foci of the hyper bola to be plotted, a hyperbola plotting cord extending between the guide means guidingly receivedby said guidesmeans, withfits end por tions extending beyond the guide means, rotary cord movement controlling means mounted on the pl'ottingboard comprising cordwinding drum cord at any point selected as a starting point'of V the hyperbole. and the relative different distances between the said selected point and the guide means for the plotting cord constituting the distancebetween the foci and the hyperbola.

Q means having 'both end portions of thecord EDWARD MCKABA. 

